(-5+5i)+(4-4i)

2 min read Jun 16, 2024

Adding Complex Numbers: (-5 + 5i) + (4 - 4i)

This article will guide you through the process of adding two complex numbers: (-5 + 5i) and (4 - 4i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers, and 'i' is the imaginary unit, defined as the square root of -1 (i² = -1).

Adding Complex Numbers

To add complex numbers, we simply add the real parts and the imaginary parts separately.

Step 1: Identify the real and imaginary parts of each complex number.

(-5 + 5i): Real part = -5, Imaginary part = 5
(4 - 4i): Real part = 4, Imaginary part = -4

Step 2: Add the real parts: -5 + 4 = -1 Step 3: Add the imaginary parts: 5 - 4 = 1

Step 4: Combine the results: (-1) + (1)i

Solution

Therefore, the sum of (-5 + 5i) and (4 - 4i) is -1 + i.

Visualization

Complex numbers can be visualized on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part. Adding complex numbers geometrically involves connecting the points representing the two complex numbers and finding the endpoint of the resulting vector.

Conclusion

Adding complex numbers is a straightforward process involving adding the real and imaginary parts separately. The solution to the given problem is -1 + i. This understanding of complex number addition is crucial for various applications in mathematics, physics, and engineering.